We correct three typographical errors in our published paper [Opt. Express26, 9194 (2018)10.1364/OE.26.009194]. First, we correct the error in the Table 1. The injection coupling strength for the summarized device in the first raw is corrected to 1.5 meV. Second, we correct the listed reference 10 to "S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, "A 1.8-THz quantum cascade laser operating significantly above the temperature of ℏω/kB," Nat. Phys. 7(2), 166-171 (2011)." Third, we correct the typographical error in the quantum structure layer thickness description. The text description on quantum structure layer thickness is correct to 40.3/74.4/24.1/103.6/29.7/79.7/40.3/156.7, which is the correct number extracted from high-resolution X-ray diffraction (HRXRD) measurement and used in simulation through the manuscript. The corrections do not alter the figures and conclusions in manuscript.